Precalculus Examples

$3 x^{2} y (2 x^{2} y - 5 x + 7 - 2)$

Step 1

Subtract $2$ from $7$ .

$3 x^{2} y (2 x^{2} y - 5 x + 5)$

Step 2

Apply the distributive property.

$3 x^{2} y (2 x^{2} y) + 3 x^{2} y (- 5 x) + 3 x^{2} y \cdot 5$

Step 3

Simplify.

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Step 3.1

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 3.1.1

Move $x^{2}$ .

$3 (x^{2} x^{2}) y (2 y) + 3 x^{2} y (- 5 x) + 3 x^{2} y \cdot 5$

Step 3.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 x^{2 + 2} y (2 y) + 3 x^{2} y (- 5 x) + 3 x^{2} y \cdot 5$

Step 3.1.3

Add $2$ and $2$ .

$3 x^{4} y (2 y) + 3 x^{2} y (- 5 x) + 3 x^{2} y \cdot 5$

Step 3.2

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 3.2.1

Move $x$ .

$3 x^{4} y (2 y) + 3 (x \cdot x^{2}) y \cdot - 5 + 3 x^{2} y \cdot 5$

Step 3.2.2

Multiply $x$ by $x^{2}$ .

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Step 3.2.2.1

Raise $x$ to the power of $1$ .

$3 x^{4} y (2 y) + 3 (x^{1} x^{2}) y \cdot - 5 + 3 x^{2} y \cdot 5$

Step 3.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 x^{4} y (2 y) + 3 x^{1 + 2} y \cdot - 5 + 3 x^{2} y \cdot 5$

Step 3.2.3

Add $1$ and $2$ .

$3 x^{4} y (2 y) + 3 x^{3} y \cdot - 5 + 3 x^{2} y \cdot 5$

Step 3.3

Multiply $5$ by $3$ .

$3 x^{4} y (2 y) + 3 x^{3} y \cdot - 5 + 15 x^{2} y$

Step 4

Simplify each term.

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Step 4.1

Multiply $y$ by $y$ by adding the exponents.

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Step 4.1.1

Move $y$ .

$3 x^{4} (y \cdot y) \cdot 2 + 3 x^{3} y \cdot - 5 + 15 x^{2} y$

Step 4.1.2

Multiply $y$ by $y$ .

$3 x^{4} y^{2} \cdot 2 + 3 x^{3} y \cdot - 5 + 15 x^{2} y$

Step 4.2

Multiply $2$ by $3$ .

$6 x^{4} y^{2} + 3 x^{3} y \cdot - 5 + 15 x^{2} y$

Step 4.3

Multiply $- 5$ by $3$ .

$6 x^{4} y^{2} - 15 x^{3} y + 15 x^{2} y$